1. True or False. Justify your answer. \text { (a) }\{1,2\} \in\{\{1,2\},\{3,4\}\} \text { (b) }\{1,2,1,2,1\} \subseteq\{1,2\} \text { (c) For all sets } A \text { and } B, \text { if }|A| \leq|B| \text { , then } A \subseteq B \text { . } \text { (d) For all sets } A, B, \text { and } C, \text { if } A \neq B \text { , then } A \cap C \neq B \cap C \text { . } \text { (e) For all } x \in \mathbf{R},\lfloor 2 x\rfloor=2\lfloor x\rfloor \text { (f) Let } n \in \mathbb{Z}^{+}, \text {then }\left(3 n^{2}+3 n\right) \bmod 6=0 \text { . } \text { (g) Let } a, b \in \mathbb{Z} \text { . If } 10 \mid a b \text { , then } 10 \mid a \text { or } 10 \mid b \text { . } \text { (h) There is a set } A \text { such that }|\mathcal{P}(A)|=100 \text { . } The expressions Væ(P(x)→ Q(x)) and (VrP(x)) → (VxQ(x))logically equiva-arelent.

Solved: 1. True or False. Justify your answer. \text { (a) }\{1,2\} \in\{\{1,

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1. True or False. Justify your answer. \text { (a) }\{1,2\} \in\{\{1,2\},\{3,4\}\} \text { (b) }\{1,2,1,2,1\} \subseteq\{1,2\} \text { (c) For all sets } A \text { and } B, \text { if }|A| \leq|B| \text { , then } A \subseteq B \text { . } \text { (d) For all sets } A, B, \text { and } C, \text { if } A \neq B \text {